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主特征值与主特征向量的检验AI 解读

We establish central limit theorems for principal eigenvalues and eigenvectors under divergent spiked covariance models, and develop three two-sample tests for testing (1) the equality of principal eigenvalues, (2) the stability of eigenvalue proportions, and (3) the invariance of principal eigenvectors. One important application of our results is to understand structural breaks in large factor models. That is, when a structural break is suspected or detected, these tests…

重尾高频金融观测下的因子与特异性 VAR 波动率矩阵模型AI 解读

This paper introduces a novel process for both factor and idiosyncratic volatility matrices whose eigenvalues follow the vector auto-regressive (VAR) model. We call it the factor and idiosyncratic VAR (FIVAR) model. The FIVAR model accounts for the dynamics of the factor and idiosyncratic volatilities and includes many parameters. In addition, many empirical studies have shown that high-frequency stock returns and volatilities often exhibit heavy tails. To handle these two…

基于高频金融数据的大型波动率矩阵自适应稳健估计AI 解读

Several novel statistical methods have been developed to estimate large integrated volatility matrices based on high-frequency financial data. To investigate their asymptotic behaviors, they require a sub-Gaussian or finite high-order moment assumption for observed log-returns, which cannot account for the heavy-tail phenomenon of stock-returns. Recently, a robust estimator was developed to handle heavy-tailed distributions with some bounded fourth-moment assumption.…

机器学习能否修正期权定价模型？AI 解读

We introduce a novel two-step approach to predict implied volatility surfaces. Given any fitted parametric option pricing model, we train a feedforward neural network on the model-implied pricing errors to correct for mispricing and boost performance. Using a large dataset of S&P 500 options, we test our nonparametric correction on several parametric models ranging from ad-hoc Black–Scholes to structural stochastic volatility models and demonstrate the boosted performance…

贝叶斯因子调整稀疏回归AI 解读

Many sparse regression methods rely on an assumption that the covariates are weakly correlated, which hardly holds in many economic and financial datasets. To relax this assumption, we model the strongly correlated covariates by a factor structure: strong correlations among covariates are modeled by common factors, while the remaining variations of covariates are modeled as idiosyncratic components. We then propose a factor-adjusted sparse regression model and develop a…

增广因子模型：市场风险因子验证与债券风险溢价预测AI 解读

We study factor models augmented by observed covariates that have explanatory powers on the unknown factors. In financial factor models, the unknown factors can be reasonably well explained by a few observable proxies, such as the Fama–French factors. In diffusion index forecasts, identified factors are strongly related to several directly measurable economic variables such as consumption-wealth variable, financial ratios, and term spread. With those covariates, both the…

通过核范数正则化估计高维广义迹回归AI 解读

We study the generalized trace regression with a near low-rank regression coefficient matrix, which extends notion of sparsity for regression coefficient vectors. Specifically, given a matrix covariate X, the probability density function of the response Y is f(Y|X)=c(Y)exp(ϕ−1−Yη∗+b(η∗)), where η∗=tr(Θ∗TX). This model accommodates various types of responses and embraces many important problem setups such as reduced-rank regression, matrix regression that accommodates a panel…

非同步高频金融数据的结构化波动率矩阵估计AI 解读

Several large volatility matrix estimation procedures have been recently developed for factor-based Itô processes whose integrated volatility matrix consists of low-rank and sparse matrices. Their performance depends on the accuracy of input volatility matrix estimators. When estimating co-volatilities based on high-frequency data, one of the crucial challenges is non-synchronization for illiquid assets, which makes their co-volatility estimators inaccurate. In this paper,…

高频数据的因子GARCH–Itô模型与大型波动率矩阵预测AI 解读

Several novel large volatility matrix estimation methods have been developed based on the high-frequency financial data. They often employ the approximate factor model that leads to a low-rank plus sparse structure for the integrated volatility matrix and facilitates estimation of large volatility matrices. However, for predicting future volatility matrices, these nonparametric estimators do not have a dynamic structure to implement. In this paper, we introduce a novel Itô…

高频因子模型中高维波动率矩阵的稳健估计AI 解读

High-frequency financial data allow us to estimate large volatility matrices with relatively short time horizon. Many novel statistical methods have been introduced to address large volatility matrix estimation problems from a high-dimensional Itô process with microstructural noise contamination. Their asymptotic theories require sub-Gaussian or some finite high-order moments assumptions for observed log-returns. These assumptions are at odd with the heavy tail phenomenon…

连续与不连续杠杆效应的估计AI 解读

This paper examines the leverage effect, or the generally negative covariation between asset returns and their changes in volatility, under a general setup that allows the log-price and volatility processes to be Itô semimartingales. We decompose the leverage effect into continuous and discontinuous parts and develop statistical methods to estimate them. We establish the asymptotic properties of these estimators. We also extend our methods and results (for the continuous…

高维尖峰协方差经验特征结构的渐近理论AI 解读

We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the magnitude of spiked eigenvalues, sample size, and dimensionality. This regime allows high dimensionality and diverging eigenvalues and provides new insights into the roles that the leading eigenvalues, sample size, and dimensionality play in principal component analysis. Our results are a natural extension of those…

波动率风险溢价如何反映流动性供给与尾部风险对冲需求？AI 解读

This article provides a data-driven analysis of the volatility risk premium, using tools from high-frequency finance and Big Data analytics. We argue that the volatility risk premium, loosely defined as the difference between realized and implied volatility, can best be understood when viewed as a systematically priced bias. We first use ultra-high-frequency transaction data on SPDRs and a novel approach for estimating integrated volatility on the frequency domain to compute…

将全球行业分类标准纳入投资组合配置：基于高频数据的因子型大规模协方差估计AI 解读

We document a striking block-diagonal pattern in the factor model residual covariances of the S&P 500 Equity Index constituents, after sorting the assets by their assigned Global Industry Classification Standard (GICS) codes. Cognizant of this structure, we propose combining a location-based thresholding approach based on sector inclusion with the Fama-French and SDPR sector Exchange Traded Funds (ETF’s). We investigate the performance of our estimators in an out-of-sample…

大型投资组合风险的稳健推断AI 解读

We propose a bootstrap-based robust high-confidence level upper bound (Robust H-CLUB) for assessing the risks of large portfolios. The proposed approach exploits rank-based and quantile-based estimators, and can be viewed as a robust extension of the H-CLUB procedure (Fan et al., 2015). Such an extension allows us to handle possibly misspecified models and heavy-tailed data, which are stylized features in financial returns. Under mixing conditions, we analyze the proposed…

因子模型中的投影主成分分析AI 解读

This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employees principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to high-dimensional factor analysis, the projection removes noise components. We show that the unobserved latent factors can be more accurately estimated than the conventional PCA if the projection is genuine, or more precisely, when the factor…

大型投资组合的风险AI 解读

The risk of a large portfolio is often estimated by substituting a good estimator of the volatility matrix. However, the accuracy of such a risk estimator is largely unknown. We study factor-based risk estimators under a large amount of assets, and introduce a high-confidence level upper bound (H-CLUB) to assess the estimation. The H-CLUB is constructed using the confidence interval of risk estimators with either known or unknown factors. We derive the limiting distribution…

高维横截面检验的功效增强AI 解读

= 0 against sparse alternatives where the null hypothesis is violated only by a couple of components. Existing tests based on quadratic forms such as the Wald statistic often suffer from low powers due to the accumulation of errors in estimating high-dimensional parameters. More powerful tests for sparse alternatives such as thresholding and extreme-value tests, on the other hand, require either stringent conditions or bootstrap to derive the null distribution and often…

采用重尾似然的 GARCH 模型拟极大似然估计AI 解读

The non-Gaussian maximum likelihood estimator is frequently used in GARCH models with the intention of capturing heavy-tailed returns. However, unless the parametric likelihood family contains the true likelihood, the estimator is inconsistent due to density misspecification. To correct this bias, we identify an unknown scale parameter ηf that is critical to the identification for consistency and propose a three-step quasi-maximum likelihood procedure with non-Gaussian…

主正交补阈值化方法与高维协方差估计AI 解读

Summary The paper deals with the estimation of a high dimensional covariance with a conditional sparsity structure and fast diverging eigenvalues. By assuming a sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the principal orthogonal complement thresholding method ‘POET’ to explore such an approximate factor structure with sparsity.…

杠杆效应之谜：分解高频估计中的偏误来源AI 解读

The leverage effect refers to the generally negative correlation between an asset return and its changes of volatility. A natural estimate consists in using the empirical correlation between the daily returns and the changes of daily volatility estimated from high frequency data. The puzzle lies in the fact that such an intuitively natural estimate yields nearly zero correlation for most assets tested, despite the many economic reasons for expecting the estimated correlation…

利用高频数据估计大规模波动率矩阵以进行组合选择AI 解读

Portfolio allocation with gross-exposure constraint is an effective method to increase the efficiency and stability of selected portfolios among a vast pool of assets, as demonstrated in Fan et al (2008). The required high-dimensional volatility matrix can be estimated by using high frequency financial data. This enables us to better adapt to the local volatilities and local correlations among vast number of assets and to increase significantly the sample size for estimating…

近似因子模型中的高维协方差矩阵估计AI 解读

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By…

基于离散观测过程的跳跃检验与定位AI 解读

We propose a new nonparametric test for detecting the presence of jumps in asset prices using discretely observed data. Compared with the test in Aït-Sahalia and Jacod (2009), our new test enjoys the same asymptotic properties but has smaller variance. These results are justified both theoretically and numerically. We also propose a new procedure to locate the jumps. The jump identification problem reduces to a multiple comparison problem. We employ the false discovery rate…